Prime factorization of $$$3665$$$

Find the prime factorization of $$$3665$$$.

Start with the number $$$2$$$.

Determine whether $$$3665$$$ is divisible by $$$2$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$3$$$.

Determine whether $$$3665$$$ is divisible by $$$3$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$5$$$.

Determine whether $$$3665$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$3665$$$ by $$${\color{green}5}$$$: $$$\frac{3665}{5} = {\color{red}733}$$$.

The prime number $$${\color{green}733}$$$ has no other factors then $$$1$$$ and $$${\color{green}733}$$$: $$$\frac{733}{733} = {\color{red}1}$$$.

Since we have obtained $$$1$$$, we are done.

Now, just count the number of occurences of the divisors (green numbers), and write down the prime factorization: $$$3665 = 5 \cdot 733$$$.

The prime factorization is $$$3665 = 5 \cdot 733$$$A.